If \({\mathcal {K}}\)  is a finite set of finite algebras in \({\mathcal {V}}\) , then
there exists an \(e\ge 1\)  such that \({\mathcal {K}}\models (x^{y^e})^{y^e}=x^{y^e}\) .
For such an \(e\) , the terms \(d(x,y)=y^{x^e}\) ,
\(p(z,y,x)^{x^{e-1}}\)  and \(s^e(x_1,\dots ,x_\mathsf {d})\)  satisfy the identities
in [1]}.
Consequently, for this \(e\) ,
our \(e\) -derived forks and
(compact) \((\mathsf {d},e)\) -representations
are exactly the minority forks (called minority indices),
and the (compact) representations with minority forks defined in
[1]}.
